Decompose P/Q, Where Q Has Only Distinct Linear Factors
Write $\frac { 6 x - 4 } { ( x + 6 ) ( x + 2 ) }$

question 91

Multiple Choice

Decompose P/Q, Where Q Has Only Distinct Linear Factors
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
1) $\frac { 6 x - 4 } { ( x + 6 ) ( x + 2 ) }$
A) $\frac { A } { x + 6 } + \frac { B } { x + 2 }$
B) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ( x + 2 ) }$
C) $\frac { \mathrm { A } } { x + 6 } + \frac { \mathrm { B } } { \mathrm { x } + 2 } + \frac { \mathrm { Cx } + \mathrm { D } } { ( \mathrm { x } + 6 ) ( \mathrm { x } + 2 ) }$
D) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 2 ) ^ { 2 } }$
- $$\frac { x - 17 } { ( x - 2 ) ( x - 5 ) }$$

• A) \(\frac { A } { x + 6 } + \frac { B } { x + 2 }\)
• B) \(\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ( x + 2 ) }\)
• C) \(\frac { \mathrm { A } } { x + 6 } + \frac { \mathrm { B } } { \mathrm { x } + 2 } + \frac { \mathrm { Cx } + \mathrm { D } } { ( \mathrm { x } + 6 ) ( \mathrm { x } + 2 ) }\)
• D) \(\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 2 ) ^ { 2 } }\)
• -\[\frac { x - 17 } { ( x - 2 ) ( x - 5 ) }\]
• A) \(\frac { 5 } { x - 2 } + \frac { - 4 } { x - 5 }\)
• B) \(\frac { - 4 } { x - 2 } + \frac { 5 } { x - 5 }\)
• C) \(\frac { 5 } { x - 2 } + \frac { 4 } { x - 5 }\)
• D) \(\frac { 4 } { x - 2 } + \frac { - 5 } { x - 5 }\)

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Definitions:

Neural Impulses

Electrical signals that travel along the neurons, allowing for communication between different parts of the body and the brain.

Peripheral Nervous System

Part of the nervous system that consists of the nerves and ganglia outside of the brain and spinal cord, responsible for connecting the central nervous system (CNS) to limbs and organs.

Axons

Long, slender projections of a neuron that transmit electrical impulses away from the neuron's cell body to other neurons, muscles, or glands.

Nerve

A bundle of nerve fibers (axons and sometimes dendrites) in the peripheral nervous system.